For many years, major chains like Domino's Pizza and Papa John's International expanded across the country without putting many small rivals out of business. That began to change a few years ago, when the majors slashed pizza prices to levels that were tough to match. By 2012, the majors had a 55 percent share of the domestic pizza delivery market, up from 51.9 percent in 2007, according to market research firm NPD Group.

Now, the big guys have another weapon that most corner pizza parlors don't—a robust online ordering system. Through platforms on desktop computers and mobile devices, consumers can order pizza without picking up the phone. The system stores credit card information and keeps track of past orders, making it possible to place a delivery order in seconds.

The dominance of big chains in other restaurant categories suggests the pizza majors have a long way to go. Large quick-service chains have a 71 percent share of the sandwich market, an 82 percent share of the Mexican food market and 96 percent of the hamburger market, NPD Group estimates

At the forefront of the digital pizza push is Papa John's, which generated more than 45 percent of domestic sales through desktop and mobile orders in the third quarter—several percentage points more than Domino's. That lead is important because pizza companies can be viciously competitive, with consumers switching allegiances if they find a better deal.

Papa John's also has a good chance of holding the lead because it is the only major chain to develop a loyalty program. Simply by making orders, Papa John's customers accumulate points redeemable for free products. Starbucks has demonstrated the power of such programs, with its card now accounting for nearly a quarter of companywide sales, up from half that level a few years ago.

The loyalty Papa John's develops should make it easier to expand its domestic store footprint, even if it goes into markets where competitors already have a presence. While Domino's has roughly 5,000 domestic stores, Papa John's only has about 3,000.

What's more, Papa John's has merely begun to venture overseas, with about 1,000 restaurants accounting for some 10 percent of its operating profit, estimates Peter Saleh of Telsey Advisory Group. Domino's, meanwhile, has nearly 6,000 international stores and has expanded at a roughly 10 percent annual pace.

Shares of Papa John's aren't cheap, trading around 27 times consensus 2014 earnings. But with so much potential to expand at home and abroad, the company can comfortably maintain earnings growth of at least 15 percent for the next couple of years. That's enough to calm any fear of being burned, analysts said.